EAGER-QAC-QSA: COLLABORATIVE RESEARCH: QUANTUM SIMULATION OF EXCITATIONS, BRAIDING, AND THE NONEQUILIBRIUM DYNAMICS OF FRACTIONAL QUANTUM HALL STATES

EAGER-QAC-QSA：合作研究：激发、编织和分数量子霍尔态的非平衡动力学的量子模拟

• 批准号: 2038028
• 负责人: Armin Rahmani
• 金额: $ 12.37万
• 依托单位: Western Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-15 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2038028&HistoricalAwards=false
• 关键词: EAGER; QAC; QSA; COLLABORATIVE; RESEARCH

NONTECHNICAL SUMMARYThis award supports theoretical research on the studies of dynamics of fractional quantum Hall states using a quantum computer. Recently, we have witnessed extensive development in building quantum computing devices. These advances have allowed efficient calculations of the properties of molecular systems of a few electrons, beyond the capabilities of classical computers. On the other hand, interactions among macroscopically large numbers of electrons lead to the emergence of novel states of matter such the fractional quantum Hall effect, which arises when electrons confined to two dimensions are placed in a strong magnetic field. Interestingly, it has been shown recently that there are connections between fractional quantum Hall states and quantum gravity. The understanding of these novel phenomena requires study of the quantum dynamics of many-particle states when driven out of equilibrium. Experimental and numerical investigations of such states are particularly challenging, motivating a completely new approach. The PIs will develop quantum algorithms to simulate and study these concepts using near-term quantum computing devices. This project will create a new table-top setup to explore questions ranging from quantum dynamics to gravity.The educational component of the activity will provide opportunities for undergraduate and graduate students, particularly from underrepresented groups, to learn about quantum computing and gain hands-on computational experience with quantum circuit design using Google's open-source packages.TECHNICAL SUMMARYThis award supports theoretical research on the nonequilibrium quench dynamics and the excitations of fractional quantum Hall states using superconducting qubits. Recent advances in quantum computing devices have motivated using them to simulate quantum states. Given the long-standing challenges in studying correlated many-electron phases, it is compelling to explore the possibility of using quantum computers to investigate these states. This project examines fractional quantum Hall states by developing efficient quantum algorithms that can be implemented on near-term quantum computers.Fractional quantum Hall states are significant examples of quantum phases, where topological order arises from strong electron-electron interactions. The understanding of fractional Hall states is primarily based on insightful trial wave functions, conformal field theory methods, exact diagonalization, and the density-matrix renormalization group. Despite extensive efforts, very little is known about the many-body excitation spectrum and the far-from-equilibrium dynamics of these systems. Notably, there has been a new understanding of novel geometric properties of fractional Hall states, which relates them to concepts in gravity. Advances in quantum computing and quantum simulations provide a new avenue to study fractional Hall phases out of equilibrium. In this research, the PIs pursue two particular directions:1- Quantum algorithms to generate dynamical quantum braiding and observe its signatures in fractional Hall phases. Even in natural quantum Hall systems, controlled generation of topological excitations and observation of quantum braiding have proved quite challenging. This project opens the door to using quantum computers as an experimental platform for realizing quantum braiding.2- Generating and observing signatures of geometric high-energy excitations, such as the putative emergent graviton in fractional quantum Hall states. To this end, the research utilizes the simulation of nonequilibrium geometric quenches of fractional Hall states on quantum computers.The PIs will use the network available at City College to involve high-school, undergraduate, and graduate students from underrepresented groups in the efforts to develop quantum algorithms. The PIs engage undergraduate students in this research, allowing them to gain authentic experience and independent research credit toward graduation. In particular, both PIs will use publicly available resources from Google AI lab to train the students in using software packages to design quantum algorithms and visualize them in terms of quantum gates.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要该奖项支持使用量子计算机研究分数量子霍尔态动力学的理论研究。 最近，我们见证了构建量子计算设备的广泛发展。这些进步使得能够有效地计算几个电子的分子系统的特性，超出了经典计算机的能力。另一方面，宏观上大量电子之间的相互作用导致出现新的物质状态，例如分数量子霍尔效应，当仅限于二维的电子被置于强磁场中时，就会出现这种现象。有趣的是，最近的研究表明，分数量子霍尔态和量子引力之间存在联系。要理解这些新现象，需要研究失去平衡时多粒子态的量子动力学。对这种状态的实验和数值研究特别具有挑战性，激发了一种全新的方法。 PI 将开发量子算法，使用近期量子计算设备来模拟和研究这些概念。该项目将创建一个新的桌面设置，以探索从量子动力学到重力的各种问题。该活动的教育部分将为本科生和研究生，特别是来自代表性不足的群体的本科生和研究生提供了解量子计算并获得实践机会使用 Google 开源包进行量子电路设计的计算经验。技术摘要该奖项支持使用超导量子位进行非平衡失超动力学和分数量子霍尔态激发的理论研究。量子计算设备的最新进展促使人们使用它们来模拟量子态。 鉴于研究相关多电子相方面长期存在的挑战，探索使用量子计算机研究这些状态的可能性迫在眉睫。该项目通过开发可在近期量子计算机上实现的高效量子算法来研究分数量子霍尔态。分数量子霍尔态是量子相的重要示例，其中拓扑顺序由强电子-电子相互作用产生。对分数霍尔态的理解主要基于富有洞察力的试验波函数、共形场论方法、精确对角化和密度矩阵重正化群。尽管付出了广泛的努力，但人们对这些系统的多体激发谱和远离平衡动力学知之甚少。值得注意的是，人们对分数霍尔态的新颖几何特性有了新的理解，这将它们与重力概念联系起来。量子计算和量子模拟的进步为研究不平衡的分数霍尔相提供了新的途径。在这项研究中，PI 追求两个特定的方向：1- 量子算法来生成动态量子编织并观察其在分数霍尔相位中的特征。即使在自然量子霍尔系统中，拓扑激发的受控生成和量子编织的观察也被证明相当具有挑战性。 该项目为使用量子计算机作为实现量子编织的实验平台打开了大门。2-生成和观察几何高能激发的特征，例如分数量子霍尔态中假定的涌现引力子。为此，该研究利用量子计算机上模拟分数霍尔态的非平衡几何淬灭。PI 将利用城市学院提供的网络，让来自代表性不足群体的高中生、本科生和研究生参与开发量子算法。 PI 让本科生参与这项研究，让他们在毕业时获得真实的经验和独立研究学分。特别是，两位 PI 将利用 Google AI 实验室的公开资源来培训学生使用软件包设计量子算法，并以量子门的方式将其可视化。该奖项反映了 NSF 的法定使命，并通过评估被认为值得支持利用基金会的智力优势和更广泛的影响审查标准。

项目成果

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

在超导量子处理器上编织分数量子霍尔准空穴

• DOI: 10.1103/physrevb.108.064303
• 发表时间: 2023
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Kirmani, Ammar;Wang, Derek S.;Ghaemi, Pouyan;Rahmani, Armin
• 通讯作者: Rahmani, Armin

Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

探测量子计算机上分数量子霍尔态的几何激发

• DOI: 10.1103/physrevlett.129.056801
• 发表时间: 2022
• 期刊: Physical Review Letters
• 影响因子: 8.6
• 作者: Kirmani, Ammar;Bull, Kieran;Hou, Chang-Yu;Saravanan, Vedika;Saeed, Samah Mohamed;Papić, Zlatko;Rahmani, Armin;Ghaemi, Pouyan
• 通讯作者: Ghaemi, Pouyan

Creating and Manipulating a Laughlin-Type ν=1/3 Fractional Quantum Hall State on a Quantum Computer with Linear Depth Circuits

在具有线性深度电路的量子计算机上创建和操纵 Laughlin 型 δ=1/3 分数量子霍尔态

• DOI: 10.1103/prxquantum.1.020309
• 发表时间: 2020
• 期刊: PRX Quantum
• 影响因子: 9.7
• 作者: Rahmani, Armin;Sung, Kevin J.;Putterman, Harald;Roushan, Pedram;Ghaemi, Pouyan;Jiang, Zhang
• 通讯作者: Jiang, Zhang